Is there any outdoor square dance audio that supports lossless format music?

MP3 sound quality is just fine, there is no need for lossless format.

Because most speakers are not lossless speakers, even if you have the top of the line CD player with CD masters, you can't listen to lossless music without first class audio.

So lossless music just doesn't make sense, and you won't hear much difference with a regular stereo.